All x satisfying the inequality ( cot-1 x)2 - 7 ( cot-1 x)+10 0 lie in the interval :

Question

All x satisfying the inequality ( cot-1 x)2 - 7 ( cot-1 x)+10 > 0 lie in the interval : (A) (- ∞ , cot 5) ∪ ( cot 4, cot 2) (B) (cot 5, cot 4) (C) (cot 2, ∞) (D) (-∞, cot 5) ∪ ( cot 2, ∞)

Tardigrade Admin · Accepted Answer

cot-1x>5 , cot-1x <2 ⇒ x < cot5 , x > cot2

Q. All $x$ satisfying the inequality $(cot^{- 1} x)^{2} - 7 (cot^{- 1} x) + 10 > 0$ lie in the interval :

$(- \infty, cot 5) \cup (cot 4, cot 2)$

$(co t 5, co t 4)$

$(co t 2, \infty$ )

$(- \infty, cot 5) \cup (cot 2, \infty)$

$cot^{- 1} x > 5, cot^{- 1} x < 2$
$\Rightarrow x < cot 5, x > cot 2$

Q. All x satisfying the inequality (cot−1x)2−7(cot−1x)+10>0 lie in the interval :

(−∞,cot5)∪(cot4,cot2)

(cot5,cot4)

(cot2,∞)

(−∞,cot5)∪(cot2,∞)